{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "fed293b4",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3.4.2\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1bb75e9fbb0>]"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "print(matplotlib.__version__)\n",
    "\n",
    "nsteps = 1000\n",
    "draws = np.random.randint(0, 2, size=nsteps)\n",
    "\n",
    "steps = np.where(draws > 0, 1, -1)\n",
    "walk = steps.cumsum()\n",
    "\n",
    "plt.plot(walk[:200])"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
